Essential and continuous spectrum of symmetric difference equations

Abstract

Essential and continuous spectrum of symmetric difference equations have been investigated. It has been shown that the deficiency indices and the existence of these components of the spectrum are determined by the growth conditions of the coefficients. In particular, the deficiency indices are superimposition of those clusters determined by the coefficient growth. Finally, we have proved the neccessary and sufficient conditions for the existence of essential spectrum of selfadjoint subspace extensions using subspace theory and asymtotic summation. K E Y W O R D Ssubspaces, deficiency indices, essential spectrum, continuous spectrum M S C ( 2 0 1 0 ) Primary: 39A20, Secondary: 47A55 www.mn-journal.org